Problem: Let $a$ and $b$ be complex numbers: $\begin{align*} a &= 1 - 4i \\ b &= 3 - 4i \end{align*}$ What is $a+b$ ? 1 2 3 4 5 6 7 8 9 10 11 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 \llap{-}11 1 2 3 4 5 6 7 8 9 10 11 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 \llap{-}11 Re Im a b
Solution: Sum the real and imaginary components separately. $a + b = (1 + 3) + (-4 - 4)i$ $\hphantom{a + b} = 4 - 8i$